RATIONALIZING THE DENOMINATOR

Front

What does it mean to rationalize the denominator?

Back

To rationalize the denominator means to eliminate any irrational numbers (like square roots) from the denominator of a fraction.

Front

Why is rationalizing the denominator important?

Back

Rationalizing the denominator is important because it simplifies expressions and makes them easier to work with, especially in further calculations.

Front

How do you rationalize a denominator that contains a square root?

Back

To rationalize a denominator with a square root, multiply both the numerator and the denominator by the square root that is in the denominator.

Front

Rationalize the denominator: 1/(√2)

Back

(√2)/(2) - Multiply numerator and denominator by √2.

Front

Rationalize the denominator: 3/(√5)

Back

(3√5)/(5) - Multiply numerator and denominator by √5.

Front

What is the result of rationalizing the denominator of 5/(√3 + 1)?

Back

(5(√3 - 1))/2 - Multiply by the conjugate (√3 - 1)/(√3 - 1).

Front

What is a conjugate in the context of rationalizing denominators?

Back

A conjugate is a binomial formed by changing the sign between two terms, e.g., the conjugate of (a + b) is (a - b).

Front

Rationalize the denominator: 2/(√7 - 2)

Back

(2(√7 + 2))/(3) - Multiply by the conjugate (√7 + 2)/(√7 + 2).

Front

What is the general formula for rationalizing a denominator with a binomial?

Back

If the denominator is (a + b), multiply by (a - b)/(a - b) to rationalize.

Front

Rationalize the denominator: 4/(√6 + √2)

Back

(4(√6 - √2))/(4) - Multiply by the conjugate (√6 - √2)/(√6 - √2).